Inverter Efficiency Models

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Summary

Inverter Efficiency Models calculate conversion efficiency from DC to AC power using manufacturer-supplied efficiency curves at multiple voltage and power levels. PlantPredict implements two efficiency calculation methods: Legacy (bilinear interpolation with DC power, Versions 3-10) and Sandia (polynomial fitting with AC power, Version 11+). Both methods use bilinear interpolation across voltage and power dimensions. The efficiency curves consist of power-efficiency pairs at typically three DC voltage levels (minimum, nominal, maximum), with efficiency values typically ranging from 0.92 to 0.99 for modern inverters.

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Inputs

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Outputs

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Detailed Description

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Efficiency Curve Structure

Efficiency curves provided at three voltage levels (see figure above for example):

• Minimum voltage ($V_{min}$)
• Nominal voltage ($V_{nom}$)
• Maximum voltage ($V_{max}$)

Each curve contains power-efficiency pairs: $\{(P_i, \eta_i)\}$

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Legacy Efficiency Model (Versions 3-10)

The Legacy model uses DC power as the independent variable and applies bilinear interpolation across voltage and power dimensions.

1. Bound inputs: Constrain DC voltage and power to the range covered by the efficiency curves
2. Identify bounding curves: Find the two voltage curves that bracket the operating voltage
3. Convert curve data: Transform AC power points to DC power using the corresponding efficiency values
4. Identify bounding power points: For each voltage curve, find the two power points that bracket the operating power
5. Bilinear interpolation: Interpolate efficiency across the four corner points defined by the bounding voltages and powers

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Sandia Efficiency Model (Version 11+)

Requires at least 3 efficiency curves. Step 1: Extract voltage levels $$V_{min} = \min(\text{curve voltages})$$ $$V_{max} = \max(\text{curve voltages})$$ $$V_{nom} = \text{middle voltage}$$ Step 2: Fit quadratic polynomials for each voltage For each voltage curve, convert AC to DC power and fit: $$P_{AC} = c_0 + c_1 P_{DC} + c_2 P_{DC}^2$$ using polynomial regression (order 2). Step 3: Calculate characteristic DC powers For each curve, solve for $P_{DC}$ at maximum AC power: $$P_{DC,char} = \frac{-c_1 + \sqrt{c_1^2 - 4c_2(c_0 - P_{AC,max})}}{2c_2}$$ Step 4: Calculate S0 (no-load offset) For each curve: $$S_0 = \frac{-c_1}{2c_2}$$ Step 5: Fit linear relationships Define $x_d = [V_{min} - V_{nom}, 0, V_{max} - V_{nom}]$ Fit linear relationships:

• $P_{DC,char}$ vs $x_d$: coefficients $[a_1, b_1]$, slope factor $s_1 = b_1/a_1$
• $S_0$ vs $x_d$: coefficients $[a_2, b_2]$, slope factor $s_2 = b_2/a_2$
• $c_2$ vs $x_d$: coefficients $[a_3, b_3]$, slope factor $s_3 = b_3/a_3$

Step 6: Calculate at actual voltage $$\Delta V = V_{DC} - V_{nom}$$ $$a = a_1 (1 + s_1 \Delta V)$$ $$b = a_2 (1 + s_2 \Delta V)$$ $$c = a_3 (1 + s_3 \Delta V)$$ $$P_{AC,max,curve} = \lfloor \max(\text{AC powers from curves}) \rfloor$$ Step 7: Calculate estimated AC output $$P_{AC,est} = \frac{P_{AC,max,curve}}{a - b - c(a - b)} (P_{AC} - b) + c (P_{AC} - b)^2$$ Step 8: Calculate efficiency $$\eta = \frac{P_{AC,est}}{P_{AC}}$$ If $P_{AC} = 0$: $\eta = 0$ In Version 12 and later, the efficiency is constrained to be non-negative.

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References

• King, D. L., Boyson, W. E., & Kratochvil, J. A. (2004). Photovoltaic array performance model. SAND2004-3535, Sandia National Laboratories.
• California Energy Commission. Inverter test protocol. CEC-CSI, Version 2.2.